Question

3. A certain company operates automobile dealerships in six regions. The general manager questioned whether the mean profit margin per vehicle sold differed by region. A random sample of 5 vehicles sold in each region is selected and the profit margin of each vehicle is recorded. Given the value of the test statistic is 2.52, what do you conclude in terms of the problem)? Use a = .05. What is the P-value of your test statistic?

Answer 1

Solution:

For the given scenario, we need to use one way ANOVA.

We are given

Number of regions/groups = k = 6

Each sample size = 5

Total number of observations = N = 6*5 = 30

Total df = N – 1 = 30 – 1 = 29

Between df = k – 1 = 6 – 1 = 5

Within df = Total df – Between df = 29 – 5 = 24

We are given

Test statistic = F = 2.52

df1 = between df = 5

df2 = within df = 24

P-value = 0.057132

(by using F-table or excel)

Level of significance = α = 0.05

P-value > α = 0.05

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that the mean profit margins per vehicle sold by region are different.